A New State-Space Approach for Direction Finding

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Direction-of-arrival estimation using state-space models in sensor array processing with a uniform linear array can be reduced to finding a solution to the equation Ũ1F ≈ Ũ2 for F, where noises in both sides of the equation are highly correlated. Least squares or even total least squares solutions are not optimal, and the complicated covariance structure in Ũ1 and Ũ2 does not allow a weighted total least squares procedure to be carried out. The approach presented in this correspondence is to first solve a least squares problem to get an estimate of the underlying subspace represented by the noisy basis vectors in Ũ1 and Ũ2. An approximate error covariance matrix for the least squares problem is obtained using a first-order perturbation expansion. This covariance matrix is used to solve for the underlying subspace in a weighted least squares sense. Parameters are then extracted from the estimated subspace. Numerical examples show that the performance of the proposed method is very close to the Cramer-Rao bound. © 1994 IEEE

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IEEE Transactions on Signal Processing